_ n = 1 ^ 50 i^ 2n-1 is equal to (where i = -1 ) - Vidyadip

MCQ

$\sum\limits_{n = 1}^{50} {{i^{2n-1}}}$ is equal to (where $i = -1$ )

A
$48$
B
$48 + i$
✓
$47 + i$
D
$48+2i$

✓

Answer

Correct option: C.

$47 + i$

c
$\sum\limits_{n = 1}^{50} {{i^{2n - 1!}}} = {i^{1!}} + {i^{3!}} + {i^{5!}} + .... + {i^{99!}}$

$ = {{\rm{i}}^1} + {{\rm{i}}^6} + 1 + 1 + .... + 1$

$=\mathrm{i}-1+48=47+\mathrm{i}$

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